Causality and replication in concurrent processes

Abstract

The replication operator was introduced by Milner for obtaining a simplified description of recursive processes. The standard interleaving semantics denotes the replication of a process P, written IP, a shorthand for its unbound parallel composition, operationally equivalent to the process P | P | . . . , with P repeated as many times as needed. Albeit the replication mechanism has become increasingly popular, investigations on its causal semantics has been scarce. In our work we consider the interleaving semantics for the operator proposed by Sangiorgi and Walker, and we show how to refine it in order to capture causality. Furthermore, we prove that a basic property usually associated to these semantics, the so-called concurrency diamond, does hold in our framework, and we sketch a correspondence between our proposal and the standard causal semantics for recursive process studied in the literature, for processes defined through constant invocations. © Springer-Verlag Berlin Heidelberg 2003.